Departure to pure de Sitter geometry based on Planck data

Abstract

In this paper, we will obtain the basic parameters of primordial inflation such as power spectrum, scalar spectral index, and tensor-to-scalar ratio as a function of Hankel index [Formula: see text] for asymptotic-de Sitter inflation and then, based on the observational constraints on these parameters from Planck data, we obtain the allowable range for index [Formula: see text]. We will show that only the non-phantom phase is acceptable for quasi-de Sitter inflation at early universe. As a significant result, both of the primordial and late accelerating expansion are always in a quasi-vacuum phase (with [Formula: see text]) and it has never been in a pure-vacuum phase (with [Formula: see text]), i.e. cosmological constant. Therefore, based on our recent finding [E. Yusofi, M. Khanpour, B. Khanpour, M. A. Ramzanpour and M. Mohsenzadeh, Surface tension of cosmic voids as a possible source for dark energy, Mon. Not. R. Astron. Soc. 511 (2022) L82], we offer the surface tension of cosmic voids as a suitable alternative to the cosmological constant [Formula: see text], for accelerating universe.

Quasi-de sitter solution, negative norm state and Krein space in cosmology

“…Data from the Wilkinson probe and Planck satellite on cosmic background microwave radiation indicate that, with approximately 95% confidence, the scalar spectral index value is within the range of n s = 0.9649 ± 0.0042 [7]. Therefore, cosmologists believe that the universe, in the period of inflation, is similar to de Sitter in the first approximation [5,[8][9][10]. Since the theory of quantum fields is very closely related to early universe cosmology, it seems natural that in this branch of physics we be also seek to examine the results of new methods adopted in quantization of the fields.…”

“…On the other hand, given that the theory of quantum fields in curved space plays a significant role in the discussion of inflation, so it can be expected that the result of considering the period of quasi-de Sitter inflation can affect the initial value of the quantum fluctuations of the scalar field in the early universe [11]. In fact, these effects can be reflected in the power spectrum of temperature fluctuations in cosmic background radiation [8,[12][13][14][15][16][17][18], which today, with the help of observational information sent to us by satellites, it has provided an important tool for judging the theories and models of cosmologists [9]. Reviewing of the published paper by using our proposal, it will be shown that the choice of non-flat background geometry will have an impact on the final results.…”